Talks

Both the social and natural world are replete with complex structure that often has a probabilistic interpretation. In the former, we may seek to model, for example, the distribution of natural images or language, for which there are copious amounts of real world data. In the latter, we are given the probabilistic rule describing a physical process, but no procedure for generating samples under it necessary to perform simulation. In this talk, I will discuss a generative modeling paradigm based on maps between probability distributions that is applicable to both of these circumstances. I will describe a means for learning these maps in the context of problems in statistical physics, how to impose symmetries on them to facilitate learning, and how to use the resultant generative models in a statistically unbiased fashion. I will then describe a paradigm that unifies flow-based and diffusion based generative models by recasting generative modeling as a problem of regression. I will demonstrate the efficacy of doing this in computer vision problems and end with some future challenges and applications.

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I will review recent progress in the asymptotic safety approach to quantum gravity. This includes the computation of momentum-dependent graviton correlation functions, the structure of the Standard Model with asymptotically safe gravity, and the recent first computation directly in space-times with Lorentzian signatures via the spectral function of the graviton. Overall, I will display the progress towards the computation of the quantum effective action which encapsulates effective field theory in the IR limit and the asymptotic safety regime in the UV limit.

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In the near future, where only a small number of companies and institutions will have access to large-scale quantum computers, it is essential that clients are able to delegate their computations in a secure way, without their data being accessible by the server. The field of blind quantum computation has emerged in recent years to address this issue, however, the majority of work on this topic has so far been restricted to the secure computation of sequences of quantum gates acting on a quantum state. Yet, a client capable of performing quantum subroutines may want to conceal not only their quantum states but also the subroutines they perform themselves. In this work, we introduce a framework of higher-order blind quantum computation, where a client performs a quantum subroutine (for example a unitary gate), which is transformed in a functional way by a server with more powerful quantum capabilities (described by a higher-order transformation), without the server learning about the details of the subroutine performed. As an example, we show how the DQC1 algorithm for estimating the trace of a unitary gate can be implemented securely by a server given only an (extended) black-box description of the unitary gate. Finally, we extend the framework to the case where the details of the server's algorithm are also concealed from the client.

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A fundamental result in solid-state physics asserts that a crystalline material cannot be insulating unless the number of electrons per unit cell is an integer. Statements of this nature are immensely powerful because they are sensitive only to the general structure of the system and not to the microscopic details of the interactions. Such "kinematic constraints" have been extensively generalized in contemporary times, commonly under the term "quantum anomaly”. In this colloquium, I will first review some basic aspects of anomaly constraints in many-body quantum physics. Subsequently, I will demonstrate, through several recent examples, the significant role of quantum anomaly in constraining, understanding, and even unveiling novel quantum phases of matter.

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The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and the modularity. A major obstacle in realizing FTQC with conventional protocols, such as those based on the surface code and the concatenated Steane code, has been the space overhead, i.e., the required number of physical qubits per logical qubit. Protocols based on high-rate quantum low-density parity-check (LDPC) codes gather considerable attention as a way to reduce the space overhead, but problematically, the existing fault-tolerant protocols for such quantum LDPC codes sacrifice the other factors. Here we construct a new fault-tolerant protocol to meet these requirements simultaneously based on more recent progress on the techniques for concatenated codes rather than quantum LDPC codes, achieving a constant space overhead, a high threshold, and flexibility in modular architecture designs. In particular, under a physical error rate of 0.1%, our protocol reduces the space overhead to achieve the logical CNOT error rates 10^{−10} and 10^{−24} by more than 90% and 97%, respectively, compared to the protocol for the surface code. Furthermore, our protocol achieves the threshold of 2.4% under a conventional circuit-level error model, substantially outperforming that of the surface code. The use of concatenated codes also naturally introduces abstraction layers essential for the modularity of FTQC architectures. These results indicate that the code-concatenation approach opens a way to significantly save qubits in realizing FTQC while fulfilling the other essential requirements for the practical protocol design.

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